The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.
How to evaluate for the side length of the triangleAn equilateral triangle have all its side lengths equal so;
line AB = line BC = line AC
At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle
Line BC form the diameter of the circle which is 2 radius of the circle so;
line BC = 2 × radius of the circle
line BC = 2 × 1
line BC = 2
Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.
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What is the coordinate of the vertex of this following parabola?
Comparing the parabola's equation to the formula [tex]y = ax^2 + bx + c[/tex] in standard form is the first step. In step 2 Apply the formula h = -b/2a to find the vertex's x-coordinate. In step 3 Substitute x = h in the expression [tex]y = ax^2 + bx + c[/tex] to obtain the vertex's y-coordinate (k).
How are the axis and vertex determined?The equation of the parabola's axis of symmetry is the vertex's x-coordinate. The axis of symmetry for a quadratic function in standard form, [tex]y = ax^2 + bx + c[/tex] is a vertical line, [tex]x=b^2a[/tex].
What exactly is a vertex?The intersection of two lines or rays that create an angle is known as the vertex of the angle.
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Find the slope of the line shown on each graph below
The slope of the lines that passes trough the points (-2,-1) and (-4,-7) is m = 3 , (2,-3) and (6,-13) is m = -2.5 , (-3,4) and (-3,-8) is m = undefined , (-5,7) and (3,-1) is m = -1 .
What is slope ?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b).
(-2,-1) and (-4,-7)
m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−7−−1)/(−4−−2)
m=−6/−2
m = 3
(2,-3) and (6,-13)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−13−−3)/(6−2)
m=−10/4
m=−5/2
m = -2.5
(-3,4) and (-3,-8)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−8−4)/(−3−−3)
m=−12/0
m is undefined
(-5,7) and (3,-1)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−1−7)/(3−−5)
m=−8/8
m = -1
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State the domain and range of the following function.
Answer:
Step-by-step explanation:
ur STUP1d
1: What number must be multiplied by (5x + 6) to result in the expression 20x + 24?
2: On the first day of a road trip, you drive x miles.
On Day 2, you drive 10 more than twice the miles driven on Day 1.
On Day 3, you drive 100 miles less than Day 1.
Write an expression to represent the miles driven on each day of the road trip, then write a final simplified expression representing the total miles driven in three days.
a) Day 1:
b) Day 2:
c) Day 3:
d) Final simplified expression to represent total miles driven in three days:
e) Look at your expression for c) Day 3: "100 miles less than Day 1." Describe a real-word situation to explain why order matters when writing this expression.
1. The number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is 4.
2. An expression representing the miles driven on each day of the road trip and a final simplified expression of the total drives in three days are as follows:
a) Day 1: x
b) Day 2: 2x + 10
c) Day 3: x - 100
d) Final simplified expression to represent total miles driven in three days: 4x + 10 - 100.
e) A real-world situation in which order matters when writing the expression x - 100 is that the value of x is supposed to be more than the value of 100.
What is a mathematical expression?A mathematical expression is the combination of constants, numbers, mathematical operators, and variables without the equation sign (=).
Literarily, a mathematical expression is like a phrase in the English language because it does not make complete sense without the equation sign.
1) Multiplication:
(20x + 24) ÷ (5x + 6) = 4
Check:
4(5x + 6) = 20x + 24
2) Road Trip Expressions:
Day one driving distance = x miles
Day two driving distance = 2x + 10
Day three driving distance = x - 100
Total distance = x + 2x + 10 + x - 100
= 4x + 10 - 100
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i tried using brainly but i couldnt find this question!
Answer:
dddd
Step-by-step explanation:
1) Use your own words to explain the following terms:
function,
domain, range vertical line test.
Function: A function is a mathematical relationship between two sets of values, where each element in the first set (called the domain) is related to exactly one element in the second set (called the range). A function can be represented by a formula, equation, or graph, and it describes how one set of values is related to another.
Domain: In a function, the domain is the set of all possible values that can be used as input for the function. It is the set of values that the function operates on.
Range: In a function, the range is the set of all possible values that can be produced as output by the function. It is the set of values that the function produces as a result of operating on the domain.
Vertical line test: The vertical line test is a method used to determine whether a graph represents a function.
Hope This Helps You!
any help please - Simplify the expression 3(x + 2) –5(2x + 1). Factorise the expression 12x –18y and 2x2–5x –3. (3+6=9)
Simplifying the expression, the answer would be -7x+1
Solution
3 (x+2) - 5 (2x+1)
3x + 6 - 10x -5
COLLECT LIKE TERMS
3x - 10x + 6 - 5
= -7x+1
Which value of x makes the expression equal.
5x, 7x - 6
Answer: x=3
Step-by-step explanation:
5x=7x-6
6+5x=7x
6=7x-5x
6=2x
solve for x which x=3
Answer:
x = 3
Step-by-step explanation:
Set the equations equal to each other:
5x = 7x - 6
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Division
Addition
Subtraction
~
Subtract 7x from both sides of the equation:
[tex]5x (-7x) = 7x (-7x) - 6\\5x -7x = -6\\-2x = -6[/tex]
Next, divide -2 from both sides of the equation:
[tex]\frac{-2x}{-2} = \frac{-6}{-2}\\ x = \frac{-6}{-2}[/tex]
*Remember that, when you divide two negative numbers, your answer will be positive:
[tex]x = \frac{-6}{-2} = 3[/tex]
3 is your answer for x.
x = 3.
~
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What is the greatest common factor of 3x
Answer:
It is not possible to find the greatest common factor of 3x.
Step-by-step explanation:
The greatest common factor (GCF) of a set of numbers is the largest number that divides into all of the numbers in the set.
In this case, you have provided a variable, 3x, and not a set of numbers. Therefore, it is not possible to find the greatest common factor of 3x.
If you have a set of numbers that you would like to find the greatest common factor of, please let me know and I will be happy to help.
Solve for x.
A: 14
B: 8
C: 11
D: 9
An acute triangle is made up of three acute angles. An obtuse triangle is formed by one acute angle and two obtuse angles and x = 9.7692307692
what is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. In Euclidean geometry, any three points identify a distinct triangle and, concurrently, a distinct plane if they are not collinear.
13x + 3 + 40 + 10 = 180
13x = 127
x = 9.7692307692
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What is the common denominator of y + StartFraction y minus 3 Over 3 EndFraction in the complex fraction y + StartFraction y minus 3 Over 3 EndFraction divided by five-ninths + StartFraction 2 Over 3 y EndFraction?
The common denominator of the given expression is 5y+6.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, we have,
Given expression,
(y+(y-3)/3)/(5/9+2/3y)
We have to find the common denominator.
On solving the numerator and denominator of the given expression,
=3y(4y-3)/5y+6
Hence the common denominator of the above expression is given by 5y+6
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Dan is training his puppy, Lola, to sit. Dan holds a treat 5 feet above the ground until Lola
sits. As soon as she does, he drops the treat, and Lola catches it in her mouth 1.5 feet above
the ground.
To the nearest tenth of a second, how long does the treat fall before Lola catches it?
Hint: Use the formula h = -16t² + s.
Answer:
t = 0.5 seconds
Step-by-step explanation:
Given formula:
[tex]h=-16t^2+s[/tex]
where:
h = height above the ground (in feet)t = time after dropping the treat (in seconds)Dan drops the treat 5 feet above the ground.
Therefore, when t = 0, h = 5 ft.
To find the value of s, substitute these values into the given formula:
[tex]\implies -16(0)^2+s=5[/tex]
[tex]\implies s=5[/tex]
Therefore:
[tex]h=-16t^2+5[/tex]
To calculate how long the treat falls before Lola catches it, substitute h = 1.5 into the formula:
[tex]\implies -16t^2+5=1.5[/tex]
[tex]\implies -16t^2=-3.5[/tex]
[tex]\implies t^2=0.21875[/tex]
[tex]\implies t=\sqrt{0.21875}[/tex]
[tex]\implies t=\pm0.467707173...[/tex]
[tex]\implies t=\pm0.5\; \; \sf (nearest\;tenth)[/tex]
As time is positive, t = 0.5 seconds (nearest tenth) only.
Therefore, it took 0.5 seconds for Lola to catch the treat after it fell.
What is the value of k?
1/2k + 6 = 4k - 8
Answer:
k=4
Step-by-step explanation:
[tex] \frac{1}{2} k - \frac{4}{1} k = - 8 - 6[/tex]
[tex] \frac{(1 \times 1) - (4 \times 2)}{(2 \times 1)} k = - 14[/tex]
[tex] \frac{1 - 8}{2}k = - 14[/tex]
[tex] - \frac{7}{2} k = - 14[/tex]
[tex] \frac{ - \frac {7}{2} }{ - \frac{7}{2} }k = \frac{ - 14}{ - \frac{7}{2} } [/tex]
[tex]k = 4[/tex]
n x (5 + 3) = (6 x 5) + (6 x 3) write the missing number.
Answer:
6 is the missing number
Step-by-step explanation:
Solve what is inside of the parenthesis, then evaluate.
N x (8) = (30) + (18)
8N = 48
Solve for N.
N = 48/8
N = 6
(7/8 x 14) / (3/8 x 6) + 2 1/5
Answer:
7/8 x 14= 12.25 or 49/4 or 12 1/4
(3/8 x 6) + 2 1/5= 4.45
(hope this helps I probably wasn't fully understanding)
Please help will mark Brainly
Answer:
371 children
Step-by-step explanation:
289*$2,5 + 371*$1,5 = $1279
please help asap
will give brainliest
Answer:
m<D should also be 98° due to the congruent angles theorem
Answer:
98
Step-by-step explanation:
Sides AB and DC are parallel.
Sides AD and BC are parallel.
Quadrilateral ABCD is a parallelogram.
Opposite angles of a parallelogram are congruent.
m<D = m<B = 98°
Answer: 98
My question is in the pic
Answer: 7t+7
Step-by-step explanation: i know
Well, both 4t and 3t have the same variable so add them together to get 7t, then add 4 and 3 to get 7, so your fill in the blank should be 7t+7
Solve each equation for both variables help please 15 points
Answer:
x = 12 and y = 11
Step-by-step explanation:
4x+3y=-15 -----equation 1st
4x-y = -27 ____equation 2nd
then,
Multiple equation second by 3 and slove it with equation first
4X +3Y = -15
12X -3Y = -81 (Multiples it with 3)
-8x = -96 (subtracted)
x=-96/-8
therefore, x=12
again,
from equation first
4x+3y = -15
or 4 × 12 + 3y = -15
or 3y = -15+48
or 3y= 33
or y=33/3
therefore, y =11
I hope this helps. If you have any doubt feel free to ask!!
Answer:
x = -6, y = 3
Step-by-step explanation:
1) 4x + 3y = -15
2) 4x - y = -27
0 + 4y = 12 subtract equation (2) from equation (1)
4y = 12
y = 12/4 = 3 substitute y = 3 into either equation 1 or 2 and solve for x
4x + 3(3) = -15
4x = -24
x = -6
Check your answers by plugging x = -6, y = 3 into the equations:
4(-6) + 3(3) = -15 correct!
4(-6) - 3 = -27 correct!
Six bottles of water cost £2.10. How much does one bottle of water cost?
There are a total of 32 books and calculators on a table. The ratio of the number of books to the
number of calculators is 5: 3. How many calculators are on the table?
A. 3
B. 12
C. 20
D. 24
Answer:
B. 12
Step-by-step explanation:
Your ratio of 5:3 means that the ratio includes 8 objects (5+3). If you multiply the whole ratio by 4, then you have 32 objects on your table. Multiplying your ratio by 4 gives you 5*4 : 3*4 which is 20:12. and since 20 is your amount of books and 12 is your amount of calculators, you have 12 calculators on your table.
Keshawn is organizing textbooks on his bookshelf. He has a Spanish textbook, a biology textbook, a history textbook, and a writing textbook. How many different ways can he line the textbooks up on his bookshelf?
Answer: four textbooks
Step-by-step explanation:
13. Communicate and Justify During a chemistry experiment, Julian
records how the temperature changes over time using ordered
pairs (time in minutes, temperature in °C).
(0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100)
a. Which variable is the independent variable?
The dependent variable? Explain in need answerssss
Julian uses ordered pairs to record the temperature variations over time during a chemistry experiment (time in minutes, temperature in °C). (0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100) (25, 100).
What do you meant by depend and independent variable ?It is the cause that is the independent variable. Its worth is unrelated to other study variables. The effect serves as the dependent variable. The independent variable's modifications determine its value. It is a thing that is dependent on other things. The amount of study you did, how much sleep you had the night before the test, or even how hungry you were when you took it.
Could all affect your test result, which makes it a dependent variable. The dependent variable is impacted by the independent variable. For instance, your exam results are influenced by how much sleep you get (an independent variable) (dependent variable). This is understandable, but Ex. How much sleep you get depends on your test results.
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cesar is making a solution for his chenistry class. he puts 3/4 gram sodium chloride and 1/3 gram potassium chloride on the scale. what is the combined mass of the compounds?
The combined mass of the compounds is 13/12 grams
How to determine the combined mass of the compounds?From the question, we have the following parameters that can be used in our computation:
3/4 gram sodium chloride and 1/3 gram potassium chloride
The combined mass of the compounds is then calculated as
Combined mass = sodium chloride + potassium chloride
Substitute the known values in the above equation, so, we have the following representation
Combined mass = 3/4 + 1/3
Evaluate the sum
Combined mass = 13/12
Hence, the combines mass is 13/12 grams
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Given that c:d is 4:3 and d:u is 2:9, find c:d:u.
Answer:
c : d : u = 8 : 6 : 27
Step-by-step explanation:
Given c:d = 4:3 and d:u = 2:9, you want c:d:u.
Ratio unitsTo write the desired ratio, we need to convert the others so they have the same number of ratio units representing 'd'. That number can be the least common multiple of 3 and 2, which is 6. Knowing this, we can write ...
c:d = 4:3 = 8:6
d:u = 2:9 = 6:27
Then the desired ratio is ...
c:d:u = 8:6:27
This graph represents a function. The linear function on a coordinate plane passes through (2, 9), and (minus 5, minus 5) which intercepts the axis at (0, 5), and (minus 2.5, 0). Which table contains points from the inverse of the graphed function? A. x -3 -1 1 3 y 1 2 3 4 B. x -4 -3 -2 -1 y -3 -1 1 3 C. x 1 2 3 4 y -3 -1 1 3 D. x -3 -1 1 3 y -4 -3 -2 -1
Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?
To determine how much it will cost Aftab to buy enough concrete slabs to make the patio, you will need to know the size of the patio and how many slabs are needed to cover it. Once you have this information, you can multiply the number of slabs by the cost per slab to find the total cost. For example, if the patio is 10 square meters and requires 20 concrete slabs to cover it, the total cost would be 3.10 * 20 = £62.
A rope 15 inches long has been divided into the greatest possible number of pieces in such a way that each piece has a different length, and each of these lengths in inches is expressed by a whole number. How many cuts were made?
A.3
B.4
C.5
D.6
E.7
Answer:
Below
Step-by-step explanation:
1+2+3+4+5 =15 5 lengths will require 4 cuts
Tell whether the angles are adjacent or vertical. Then find the value of x.
What is an equation of the line that passes through the points (4,7) and (-3,7)
Answer:y=
Step-by-step explanation:Firstly let's find the slope which is (7-7)/(4-(-3))=0. Using the point slope formula y-y1=m(x-x1) we plug in one of the points and simplify y-7=0(x-4). Simplifying and solving for y gives us y=